rocsolver_sgerqf Interface Reference

rocsolver_sgerqf Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgerqf Interface Reference

GERQF computes a RQ factorization of a general m-by-n matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgerqf_ (handle, m, n, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgerqf_full_rank (handle, m, n, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgerqf_rank_0 (handle, m, n, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgerqf_rank_1 (handle, m, n, A, lda, ipiv)

Detailed Description

GERQF computes a RQ factorization of a general m-by-n matrix A.

(This is the blocked version of the algorithm).

The factorization has the form

\[ A = \left[\begin{array}{cc} 0 & R \end{array}\right] Q \]

where R is upper triangular (upper trapezoidal if m > n), and Q is a n-by-n orthogonal/unitary matrix represented as the product of Householder matrices

\[ Q = H_1'H_2' \cdots H_k', \quad \text{with} \: k = \text{min}(m,n). \]

Each Householder matrix \(H_i\) is given by

\[ H_i = I - \text{ipiv}[i] \cdot v_i v_i' \]

where the last n-i elements of the Householder vector \(v_i\) are zero, and \(v_i[i] = 1\).

Parameters

[in]	handle	rocblas_handle.
[in]	m	rocblas_int. m >= 0. The number of rows of the matrix A.
[in]	n	rocblas_int. n >= 0. The number of columns of the matrix A.
[in,out]	A	pointer to type. Array on the GPU of dimension lda*n. On entry, the m-by-n matrix to be factored. On exit, the elements on and above the (m-n)-th subdiagonal (when m >= n) or the (n-m)-th superdiagonal (when n > m) contain the factor R; the elements below the sub/superdiagonal are the first i - 1 elements of Householder vector v_i.
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of A.
[out]	ipiv	pointer to type. Array on the GPU of dimension min(m,n). The Householder scalars.

Member Function/Subroutine Documentation